{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 自动控制理论\n",
    "--- "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 根轨迹法  \n",
    "\n",
    "根轨迹：对于闭环系统的开环传递函数$G(s)H(s)$，当开环传递函数的某个参数变化时，其特征方程的根（开环极点）在复平面上的变化轨迹。根本来源：\n",
    "\n",
    "$$\\Phi(s) = \\frac{G(s)}{1+G(s)H(s)} \\tag{1}$$  \n",
    "令$1+G(s)H(s)$可得：  \n",
    "$$G(s)H(s)=K^*\\frac{\\prod\\limits_{j=1}^{m}(s-z_j)}{\\prod\\limits_{i=1}^{n}(s-p_i)} \\tag{2}$$\n",
    "一般是以$K^*$从零到无穷大时，对应的在复平面上的根轨迹。  \n",
    "\n",
    "### 根轨迹的绘制  \n",
    "比较繁琐，只记录根轨迹的分析与计算机绘图  \n",
    "\n",
    "#### 计算机绘图  \n",
    "首先要求出如$公式(2)$所示系统的开环传递函数，注意$K^*$实际上是分子$s^m$项的系数，要提取出来。以下式为例：  \n",
    "$$G(s)H(s)= \\frac{K^*}{s(s+0.5)(s^2+0.6s+10)}$$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "''"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "2d85c7d127c0442c9bd75cc87a61395b",
       "version_major": 2,
       "version_minor": 0
      },
      "image/png": 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",
      "text/html": [
       "\n",
       "            <div style=\"display: inline-block;\">\n",
       "                <div class=\"jupyter-widgets widget-label\" style=\"text-align: center;\">\n",
       "                    Figure\n",
       "                </div>\n",
       "                <img src='' width=640.0/>\n",
       "            </div>\n",
       "        "
      ],
      "text/plain": [
       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "from control import rlocus,tf\n",
    "from matlike import conv\n",
    "\n",
    "%matplotlib widget\n",
    "\n",
    "num = [1]\n",
    "den = conv([1,0], conv([1,0.5],[1,0.6,10]))\n",
    "\n",
    "gh = tf(num, den)\n",
    "rlocus(gh,plotstr=[])\n",
    "''"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 根轨迹图的分析  \n",
    "- 要是系统稳定，需要所有闭环极点位于复平面左侧  \n",
    "- 要使系统单调，则需所有闭环极点位于负实轴上  \n",
    "- 要使系统快速性好，则闭环极点应远离虚轴  \n",
    "- 要使系统平稳性好，要求主导极点与负实轴成$\\pm45^\\circ$角  \n",
    "- damp：阻尼  \n",
    "- 因为根轨迹是对称的，所以至分析第一二象限即可。"
   ]
  }
 ],
 "metadata": {
  "interpreter": {
   "hash": "63fd5069d213b44bf678585dea6b12cceca9941eaf7f819626cde1f2670de90d"
  },
  "kernelspec": {
   "display_name": "Python 3.9.7 64-bit",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.7"
  },
  "orig_nbformat": 4
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
